{
  "id": "1706.05647",
  "version": "v1",
  "published": "2017-06-18T13:29:58.000Z",
  "updated": "2017-06-18T13:29:58.000Z",
  "title": "Ergodicity of algebraic actions of nilpotent groups",
  "authors": [
    "Siddhartha Bhattacharya"
  ],
  "comment": "9 pages, no figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "An algebraic $\\Gamma$-action is an action of a countable group $\\Gamma$ on a compact abelian group $X$ by continuous automorphisms of $X$. We prove that any expansive algebraic action of a finitely generated nilpotent group $\\Gamma$ on a connected group $X$ is ergodic. We also show that this result does not hold for actions of polycyclic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-18T13:29:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodicity",
      "compact abelian group",
      "polycyclic groups",
      "finitely generated nilpotent group",
      "expansive algebraic action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}